Surface emitting laser

ABSTRACT

A surface emitting laser emitting a laser beam in a single transverse mode irrespective of an emission area while one-dimensionally aligning polarization of the output beam, including a two-dimensional photonic crystal, having resonance modes in directions of the primitive translation vector a 1  and a 2 , lengths |a 1 | and |a 2 | of the primitive translation vectors a 1  and a 2  satisfied |a 1 |=p×(λ 1 /2n eff1 ), |a 2 | =λ 2 /2n eff2  described by a resonance wavelengths λ 1  and λ 2  in the resonance modes in the a 1  and a 2  directions, effective refractive indexes n eff1  and n eff2  determined by the resonance modes in the a 1  and a 2  directions, an integer p of 2 or more, the resonance wavelengths λ 1  and λ 2  satisfy λ 2 ≦2×(n eff2 /(n out +n eff2 ))×λ 1  described by the effective refractive index n eff2  and a refractive index n out  of an external medium located out of the surface emitting laser.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a surface emitting laser. Particularlythe invention relates to a distributed feedback type photonic crystalsurface emitting laser that can align polarization of an output beam ina one-dimensional direction while emitting a laser beam in a singletransverse mode.

2. Description of the Related Art

One of the features of the surface emitting laser, which is one of asemiconductor laser, is that light is emitted in a perpendiculardirection or an oblique direction with respect to a substrate. Recentlythere is studied the distributed feedback (DFB) type surface emittinglaser that emits a laser beam, which resonates in an in-plane directionof the substrate, to an outside of the plane with a diffraction grating.Hereinafter, the distributed feedback type surface emitting laser isabbreviated to a DFB type surface emitting laser.

Sakai et al. (IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, vol. 23,1335 (2005)) disclose a DFB type surface emitting laser in which atwo-dimensional photonic crystal, in which a diffraction grating istwo-dimensionally formed, is used.

In the two-dimensional photonic crystal disclosed in Sakai et al., twoprimitive translation vectors have the same length. The length of theprimitive translation vector is equal to λ/n_(eff) where λ denotes anoscillation wavelength and n_(eff) denotes an effective refractive indexdetermined by the resonance mode. Since the two-dimensional photoniccrystal in which the two primitive translation vectors have the samelength forms a two-dimensional resonance mode, the DFB type surfaceemitting laser can operate in a single transverse mode regardless of asize of an emission area.

Further, since the primitive translation vector has the lengthλ/n_(eff), the two-dimensional photonic crystal acts as a second-orderdiffraction grating. A diffraction perpendicular to the plane of thetwo-dimensional photonic crystal layer is generated by the first-orderdiffraction, and an in-plane diffraction is generated by thesecond-order diffraction.

Therefore, the laser light amplified by the in-plane diffraction isperpendicularly emitted by the first-order diffraction. In theperpendicularly-emitted laser beam, polarization reflectstwo-dimensional resonance, namely, the polarization includestwo-dimensional vector components. Sakai et al. discloses an azimuthallypolarized beam.

The reason the polarization direction becomes two-dimensional will bedescribed in the following paragraphs by taking the two-dimensionalphotonic crystal of the related art disclosed in Sakai et al. as anexample.

FIGS. 9A to 9C are three-dimensional schematic diagrams illustrating areciprocal lattice space of the two-dimensional photonic crystal of arelated art in which lattice points are arrayed into a square lattice.The numerals X1 and X2 designate primitive translation vectors in thereciprocal lattice space.

The diffraction of a TE-polarized wave vector k1 travelling in an X1direction will be described with reference to FIG. 9A. The wave vectork1 becomes a diffracted wave k1′ in the perpendicular direction by thefirst-order diffraction. Since the polarization is maintained before andafter the diffraction, the polarization direction of the diffracted wavek1′ is perpendicular to both the X1 direction and the k1′ direction. Thepolarization is expressed by a dotted-line arrow. At the same time, adiffracted wave k1″ travelling in a direction opposite to the diffractedwave k1 by 180 degrees is also generated by second-order diffraction,but the diffracted wave k1″ is not involved in the polarization of thelight emitted in the perpendicular direction. The diffracted wave k1″contributes to an amplification effect in a gain region.

Similarly the diffraction of a wave vector k2 travelling in an X2direction will be described with reference to FIG. 9B. The wave vectork2 becomes a diffracted wave k2′ in the perpendicular direction by thefirst-order diffraction. The polarization direction is maintained, andthe diffracted wave k2′ has the polarization oscillating in a directionperpendicular to both the X1 direction and the k2′ direction. At thesame time, a diffracted wave k2″ travelling in a direction opposite tothe diffracted wave k2 by 180 degrees is also generated by thesecond-order diffraction.

Since the first-order diffraction of the diffracted wave k1′ and thefirst-order diffraction of the diffracted wave k2′, which contribute tothe perpendicular emission, are simultaneously generated, the diffractedwave k1′ and the diffracted wave k2′ are coupled in a wave k′ emitted inthe perpendicular direction as illustrated in FIG. 9C. That is, the wavek′ becomes the polarization in which the two-dimensional components arecombined.

SUMMARY OF THE INVENTION

In the DFB type surface emitting laser in which the two-dimensionalphotonic crystal is used, only the laser beam having the two-dimensionalpolarization direction is obtained while the laser beam is emitted inthe single transverse mode. In the case that the laser beam having thetwo-dimensional polarization is incident to a birefringence opticalelement, unfortunately an aberration is caused by the polarization.

On the other hand, in the surface emitting laser in which theone-dimensional photonic crystal is used, since only the unidirectionaldiffraction exists, the output beam inevitably has the one-dimensionalpolarization. However, in the surface emitting laser in which theone-dimensional photonic crystal is used, when the emission area isenlarged, the transverse mode becomes a multimode.

An object of the invention is to provide a DFB type surface emittinglaser that can emit the laser beam in the single transverse modeirrespective of the emission area while one-dimensionally aligning thepolarization of the output beam.

A surface emitting laser according to an aspect of the inventionincludes a two-dimensional photonic crystal that includes a resonancemode in an in-plane direction, wherein the two-dimensional photoniccrystal includes two primitive translation vectors of a primitivetranslation vector a₁ and a primitive translation vector a₂, whichextend in different directions, the resonance mode includes at least aresonance mode in a direction in which the primitive translation vectora₁ extends and a resonance mode in a direction in which the primitivetranslation vector a₂ extends, the primitive translation vector a₁ has alength |a₁|, the primitive translation vector a₂ has a length |a₂|, thelength |a₁| satisfies a relational expression |a₁|=p×(λ₁/2n_(eff1)) thatis described by a resonance wavelength λ₁ in the resonance mode in thea₁ direction, an effective refractive index n_(eff1) determined by theresonance mode in the a₁ direction, and an integer p of 2 or more, thelength |a₂| satisfies a relational expression |a₂|=λ₂/2n_(eff2) that isdescribed by a resonance wavelength λ₂ in the resonance mode in the a₂direction and an effective refractive index n_(eff2) determined by theresonance mode in the a₂ direction, and the resonance wavelength λ₁ andthe resonance wavelength λ₂ satisfy a relational expressionλ₂≦2×(n_(eff2)/(n_(out)+n_(eff2)))×λ₁ that is described by the effectiverefractive index n_(eff2) and a refractive index n_(out) of an externalmedium located out of the surface emitting laser.

According to the invention, the DFB type surface emitting laser that canemit the laser beam in the single transverse mode irrespective of theemission area while one-dimensionally aligning the polarization of theoutput beam can be fabricated.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of a surface emitting laser according to afirst embodiment.

FIG. 2 is a plan view of a two-dimensional photonic crystal layer of thefirst embodiment.

FIG. 3 is a view illustrating a photonic band of the first embodiment.

FIGS. 4A, 4B, and 4C are three-dimensional schematic diagrams of areciprocal lattice space expressing a diffraction phenomenon of thefirst embodiment.

FIG. 5 is a plan view of the reciprocal lattice space of the firstembodiment.

FIG. 6 is a view illustrating a far field pattern and a polarizationdirection of the surface emitting laser of the first embodiment.

FIG. 7A is a plan view of a two-dimensional photonic crystal layeraccording to a second embodiment.

FIG. 7B is a view illustrating a far field pattern and a polarizationdirection of the surface emitting laser of the second embodiment.

FIG. 8A is a plan view of a two-dimensional photonic crystal layeraccording to a third embodiment.

FIG. 8B is a view illustrating a far field pattern and a polarizationdirection of the surface emitting laser of the third embodiment.

FIGS. 9A, 9B, and 9C are three-dimensional schematic views of areciprocal lattice space expressing a diffraction phenomenon of therelated art.

DESCRIPTION OF THE EMBODIMENTS

Preferred embodiments of the present invention will now be described indetail in accordance with the accompanying drawings.

First Embodiment

A surface emitting laser according to a first embodiment of theinvention will be described below.

A structure of the surface emitting laser of the first embodiment willbe described with reference to FIG. 1. In a surface emitting laser 100of the first embodiment, an n-type clad layer 102, an active layer 103,a two-dimensional photonic crystal layer 104, a p-type clad layer 105,and a contact layer 106 are sequentially stacked on a substrate 101. Inthe substrate 101, an n-side electrode 107 is formed on a surfaceopposite the active layer 103. In the contact layer 106, a p-sideelectrode 108 is formed on a surface opposite the active layer 103. Aguided layer (not illustrated) can also be provided between the n-typeclad layer 102 and the active layer 103 or between the p-type clad layer105 and the active layer 103, and the guided layer has a refractiveindex higher than that of the n-type clad layer 102 and the p-type cladlayer 105. The p-type clad layer 105 can be eliminated as long as thelight is confined in a stacked direction.

For example, the substrate 101, the n-type clad layer 102, the activelayer 103, the p-type clad layer 105, and the contact layer 106 are madeof a semiconductor material containing one of elements Al, In, Ga, N,As, P, Sb, B, C, Si, Ge, and Sn. In the first embodiment, the substrate101 is made of GaN, the n-type clad layer 102 is made of AlGaN, theactive layer 103 is made of InGaN, the p-type clad layer 105 is made ofAlGaN, and the contact layer 106 is made of GaN.

An outside of the surface emitting laser 100, namely, the outsides ofthe n-side electrode 107 and the p-side electrode 108 are covered withan external medium 109.

A structure of the two-dimensional photonic crystal layer of the firstembodiment will be described with reference to FIG. 2.

As illustrated in FIG. 2, in the two-dimensional photonic crystal layer104 of the first embodiment, cylindrical low refractive index media 111are arrayed into a rectangular lattice shape in a high refractive indexmedium 110. The lattice shape can be an oblique lattice to obtain thesame effect. For example, the high refractive index medium 110 is madeof a semiconductor material containing one of elements Al, In, Ga, N,As, P, Sb, B, C, Si, Ge, and Sn. The low refractive index medium 111 hasa refractive index lower than that of the high refractive index medium110. For example, air or SiO₂ is used as the low refractive index medium111. In the first embodiment, the high refractive index medium 110 ismade of GaN, and the low refractive index medium 111 is made of air.

The rectangular lattice of FIG. 2 includes two primitive translationvectors a₁ and a₂. Since the primitive translation vectors a₁ and a₂differ from each other in a length, the two-dimensional photonic crystalhas at least a resonance mode in an a₁ direction and a resonance mode inan a₂ direction, and the resonance modes are not directly opticallycoupled. In other words, the resonance mode attributed to a diffractiongrating in the a₁ direction and the resonance mode attributed to adiffraction grating in the a₂ direction can independently be controlled,and different functions can be provided to the diffraction gratings,respectively.

In view of above, in the present invention, the diffraction grating inthe a₁ direction has a function of emitting light having a wavelength λ₁to the outside of the plane. On the other hand, the diffraction gratingin the a₂ direction has a function of controlling a transverse mode ofthe laser by a refractive index periodic structure. At this point, thediffraction grating in the a₂ direction has a period such that the lighthaving the wavelength λ₁ is not diffracted to the outside of the plane.Therefore, the surface emitting laser that emits the laser beam in thesingle transverse mode while the polarization of the output beam isaligned in the one-dimensional direction can be fabricated.

The length of the primitive translation vector a₁ in the diffractiongrating in the a₁ direction will be described. In the first embodiment,|a₁| is set to the length satisfying a relational expression|a₁|=p×(λ₁/2n_(eff1)) where |a₁| denotes the length of the primitivetranslation vector a₁, λ₁ denotes a resonance wavelength of theresonance mode in the a₁ direction, n_(eff1) denotes an effectiverefractive index determined by the resonance mode in the a₁ directionand p denotes an integer of 2 or more.

In the first embodiment, because of p=2 and |a₁|=161.35 nm, the lighthaving the wavelength λ₁=405 nm generated from the active layer 103 isdiffracted in a direction perpendicular to the surface by first-orderdiffraction, and the light is diffracted in an in-plane direction of a180-degree turn by second-order diffraction.

The length of the primitive translation vector a₂ in the diffractiongrating in the a₂ direction will be described. In the first embodiment,|a₂| is set to the length satisfying a relational expression|a₂|=λ₂/2n_(eff2) where |a₂| denotes the length of the primitivetranslation vector a₂, λ₂ denotes a resonance wavelength of theresonance mode in the a₂ direction and n_(eff2) denotes an effectiverefractive index determined by the resonance mode in the a₂ direction.

Additionally, the resonance wavelength λ₁ and the resonance wavelengthλ₂ are set so as to satisfy a relational expressionλ₂≦2×(n_(eff2)/(n_(out)+n_(eff2)))×λ₁ that is described by the effectiverefractive index n_(eff2) and a refractive index n_(out) of the externalmedium 109.

When the conditions are satisfied, the light having the wavelength λ₁ isnot diffracted to the outside of the plane by the diffraction gratingformed in the a₂ direction. That is, the polarization of the laser beamhaving the wavelength λ₁, which is emitted to the outside of the planefrom the surface emitting laser 100, can be formed only by aone-dimensional component.

The diffraction phenomenon will be described with reference to FIG. 3.

FIG. 3 is a view illustrating a photonic band diagram in an X1 directionand an X2 direction. The X1 direction and the X2 direction expressprimitive reciprocal lattice vectors, the X1 direction corresponds tothe a₁ direction of a real space, and the X2 direction corresponds tothe a₂ direction of the real space. A frequency f₁ corresponds to theresonance wavelength λ₁, and a frequency f₂ corresponds to the resonancewavelength λ₂. D₂ is a dispersion curve based on the diffraction gratingin the a₂ direction, and D_(out) is a light line determined by therefractive index n_(out) of the external medium 109 located out of thesurface emitting laser 100.

f_(x) is a frequency at an intersection point of the dispersion curve D₂and the light line D_(out). The frequency f_(x) larger than thefrequency f₁ may be the condition that the light having the frequency f₁corresponding to the resonance wavelength λ₁ is not output to theoutside of the plane by the diffraction in the X2 direction.

This will be described below using equations.

The dispersion curve D₂ folded at a point X2 is expressed by thefollowing equation 1.

D ₂=−(1/n _(eff2))×k+2/n _(eff1)×(λ₁/λ₂)  (equation 1)

On the other hand, the light line D_(out) is expressed by the followingequation 2.

D _(out)=1/n _(out) ×k  (equation 2)

Therefore, the frequency f_(x) at the intersection point of thedispersion curve D₂ and the light line D_(out) is expressed by thefollowing equation 3.

f _(x)=2×(n _(eff2) /n _(eff1))×(1/(n _(out) +n_(eff2)))×(λ₁/λ₂)  (equation 3)

Because of f₁≦f_(x), the following equation 4 is derived.

λ₂≦2×(n _(eff2)/(n _(out) +n _(eff2)))×λ₁  (equation 4)

In the first embodiment, the external medium is air, and the air hasrefractive index n_(out) of 1. Therefore, the following equation 5 isderived.

λ₂≦2×(n _(eff2)/(1+n _(eff2)))×λ₁  (equation 5)

When the relationship of the equation 5 is transformed into a relationalexpression of |a₁| and |a₂|, the following equation 6 is obtained.

|a ₂|≦2×n _(eff1)/(1+n _(eff2))×|a ₁|  (equation 6)

In the first embodiment, |a₂|=78.13 nm and λ₂=400 nm.

The diffraction phenomena in the diffraction gratings formed in the a₁direction and a₂ direction will be described along with the polarizationdirection with reference to FIGS. 4A, 4B, and 4C.

FIGS. 4A, 4B, and 4C three-dimensionally illustrate a reciprocal latticespace corresponding to the two-dimensional photonic crystal structure ofthe first embodiment, and schematically illustrate the diffractionphenomenon in the two-dimensional photonic crystal. In FIGS. 4A, 4B, and4C, the polarization is expressed by a dotted-line arrow.

The diffraction of a wave vector k1 equal to wavelength λ₁ travelling inthe X1 direction will be described with reference to FIG. 4A. The wavevector k1 becomes a diffracted wave k1′ in the perpendicular directionby the first-order diffraction. Since the polarization is maintainedbefore and after the diffraction, the polarization direction of thediffracted wave k1′ is perpendicular to both the X1 direction and thek1′ direction. The second-order diffraction is also generated at thesame time as the first-order diffraction is generated, a diffracted wavek1″ travelling in a direction opposite to the diffracted wave k1 by 180degrees is generated, but the diffracted wave k1″ does not affect thepolarization of the light emitted in the perpendicular direction. Thediffracted wave k1″ contributes to an amplification effect in a gainregion.

The diffraction of a wave vector k21 having wavelength λ₂ and a wavevector k22 having wavelength λ₂, which travel in the X2 direction, willbe described with reference to FIG. 4B. The wave vector k21 becomes adiffracted wave k21′ in an out-of-plane direction by the first-orderdiffraction. However, when the diffracted wave k21′ satisfies therelationship of λ₂≦2×(n_(eff2)/(1+n_(eff2)))×λ₁, the diffracted wavek21′ is totally reflected at an interface between the air and thecontact layer 106 or the p-side electrode 108, and the diffracted wavek21′ is not output to the outside. The wave vector k22 becomes adiffracted wave k22′ travelling in the direction opposite to thediffracted wave k22 by 180 degrees by the first-order diffraction, butthe diffracted wave k22′ is not output to the outside of the plane.

As described above, only the first-order diffraction k1′ from the X1direction is involved in the wave k′ diffracted in the out-of-planedirection (in the first embodiment, the perpendicular direction). Thatis, as illustrated in FIG. 4C, the perpendicularly-output light has thepolarization that is perpendicular to both the X1 direction and k1′direction and one-dimensionally aligned.

The surface emitting laser 100 of the first embodiment can emit thelaser beam in the single transverse mode.

FIG. 5 is a plan view illustrating the reciprocal lattice space of thetwo-dimensional photonic crystal of the first embodiment. A wave vectork11 travelling in the X1 direction becomes k11′ diffracted in theperpendicular direction by a reciprocal lattice vector G11. On the otherhand, a wave vector k12 travelling in a direction slightly deviated fromthe X1 direction causes a multi-transverse mode in the case of theone-dimensional photonic crystal surface emitting laser. However, in thefirst embodiment, an optical mode is uniquely determined since theperiodic structure is formed in the X2 direction. That is, k12 ispresent as a guide mode propagating in the diffraction grating, or theoptical mode is not present in the direction of k12.

Even if a width of a surface emission area is increased, the transversemode in which the laser beam is emitted in the perpendicular directionis attributed only to k11′. This enables the single-transverse-modeoscillation. A profile of the oscillation mode can also be controlled bya gain distribution in the two-dimensional photonic crystal.

A lower limit of the length of the primitive translation vector a₂ isdetermined as follows.

Preferably a relational expression |a₂|≧λ_(s)/2n_(eff2) in which thelength of the primitive translation vector a₂ of the rectangular latticeof FIG. 2 is described by the shortest wavelength λ_(S) in an emissionwavelength region of the active layer 103, namely, λ_(S)≦λ₂ issatisfied.

In the rectangular lattice of the first embodiment, the primitivetranslation vectors a₁ and a₂ differ from each other in the length.Therefore, in the reciprocal lattice space, the primitive reciprocallattice vectors in the X1 and X2 directions differ from each other inthe length. Accordingly, the resonance mode in the a₁ direction and theresonance mode in an a₂ direction are not optically coupled. In otherwords, a carrier, which is converted into the light having the resonancewavelength λ₂ in the a₂ direction by the active layer 103, does notcontribute to the surface emission light. Although the light in theresonance mode in the a₂ direction has the advantage that the transversemode can be controlled by the diffraction grating in the a₂ direction,the light in the resonance mode in the a₂ direction is not efficientfrom viewpoint of energy efficiency of the surface emitting laser.

Therefore, preferably a relational expression |a₂|≧λ_(S)/2n_(eff2) inwhich the length of the primitive translation vector a₂ is described bythe shortest wavelength λ_(S) in the emission wavelength region of theactive layer 103, namely, λ_(S)≦λ₂ is satisfied. When the relationalexpression is satisfied, the energy efficiency can be improved by photonrecycling.

Specifically, the light having the resonance wavelength λ₂, whichresonates in the a₂ direction, is reabsorbed at the active layer 103 tobecome the carrier. Then the carrier recombines in the active layer 103and becomes the light having the resonance wavelength λ₁ which resonatesin the a₁ direction. In the phenomenon, it is necessary that theresonance wavelength λ₂ be included in an absorption band of the activelayer 103, namely, it is necessary that the resonance wavelength λ₂ beincluded in the emission wavelength band of the active layer 103, and itis also necessary that the light having the resonance wavelength λ₂ hasthe energy higher than that of the resonance wavelength λ₁ after theconversion. Therefore, preferably the relational expression λ_(S)≦λ₂≦λ₁is satisfied. λ_(S)=380 nm is obtained because an emission wavelengthregion of the active layer 103 of the first embodiment ranges from 380nm to 420 nm, and λ_(S)≦λ₂≦λ₁ is satisfied because of λ₂=400 nm andλ₁=405 nm.

A relationship among the gain of the active layer 103, λ₁, and λ₂ willbe described below. In the first embodiment, the light having theresonance wavelength λ₁, which resonates in the a₁ direction, isdiffracted in the direction perpendicular to the plane after the laseroscillation. The light having the resonance wavelength λ₂, whichresonates in the a₂ direction, can be converted into the light havingthe resonance wavelength λ₁ by the photon recycling. However, from theviewpoint of the energy efficiency, the carrier should be consumed asthe light having the resonance wavelength λ₁ from the beginning.Therefore, preferably the gain of the active layer 103 with respect tothe resonance wavelength λ₁ is larger than the gain of the active layer103 with respect to the resonance wavelength λ₂. More preferably a peakof the gain of the active layer 103 may be matched with the resonancewavelength λ₁. In the first embodiment, the peak of the gain is matchedwith the resonance wavelength λ₁.

FIG. 6 illustrates a schematic view of a far field pattern of the beamthat is perpendicularly emitted from the surface emitting laser 100 ofthe first embodiment. Although a profile of the far field depends on anoptical coupling coefficient of the diffraction grating in the a₂direction, the double-peaked beam profile exists in the a₁ direction.Although a phase of the polarization rotates by 180 degrees at each peakposition, the one-dimensional polarization in which the polarizationdirection includes only a component in the a₂ direction is obtained. Thedotted line of FIG. 6 expresses the polarization direction and thephase.

Second Embodiment

In a second embodiment, the lengths of the primitive translation vectorsa₁ and a₂ of the two-dimensional photonic crystal of the firstembodiment are changed.

The length |a₁| of primitive translation vector a₁ satisfies|a₁|=4×(λ₁/2n_(eff1)), namely, the two-dimensional photonic crystal is afourth-order diffraction grating. More specifically, in the secondembodiment, |a₁|=645.4 nm and λ₁=405 nm. The length |a₂| of theprimitive translation vector a₂ satisfies |a₂|=λ₂/2n_(eff2). Morespecifically, in the second embodiment, |a₂|=80.66 nm and λ₂=413 nm. Inthe second embodiment, since of λ₂=1.02×λ₁ and n_(eff2)=2.56, therelational expression λ₂≦2×(n_(eff2)/(1+n_(eff2)))×λ₁ is satisfied.

FIG. 7A is a plan view illustrating a two-dimensional photonic crystallayer 104 of the second embodiment. On the outside of thetwo-dimensional photonic crystal, the two-dimensional photonic crystallayer 104 includes a distributed Bragg reflector 701 that reflects thelight having the wavelengths of λ_(S) to λ₁ toward a gain region 702.The distributed Bragg reflector 701 includes a low refractive indexmedium 703 and a high refractive index medium 704. In the secondembodiment, the low refractive index medium 703 is made of air, and thehigh refractive index medium 704 is made of GaN. Using the distributedBragg reflector 701, the light having the wavelengths of λ_(S) to λ₁,which leaks to the outside of the two-dimensional photonic crystal,particularly in the a₂ direction, can be reused as the laser beam havingthe wavelength λ₁ by the photon recycling.

In FIG. 7A, the distributed Bragg reflector 701 is disposed only in thea₂ direction. Alternatively the distributed Bragg reflector may also bedisposed in the a₁ direction.

In a surface emitting laser 100 of the second embodiment, since thefourth-order diffraction grating is used in the a₁ direction, the beamemitted to the outside of the plane includes the total of three outputbeams, namely, a beam emitted in the perpendicular direction and twosymmetric beams emitted obliquely in a direction between in the a₁direction and in the perpendicular direction. Each of the three beamsincludes the one-dimensional component.

FIG. 7B illustrates a schematic view of a far field pattern of the beamthat is perpendicularly emitted from the surface emitting laser 100 ofthe second embodiment. The far field of FIG. 7B has the beam profileincluding three peaks. The one-dimensional polarization in which thepolarization direction includes only the component in the a₂ directionis obtained. The polarization phase at the central peak rotates by 180degrees with respect to the polarization phases at both end peaks. Thedotted line of FIG. 7B expresses the polarization direction and thephase.

Third Embodiment

A third embodiment will be described.

FIG. 8A is a plan view illustrating a two-dimensional photonic crystallayer 104 of the third embodiment, and the two-dimensional photoniccrystal layer 104 includes a phase shift structure having a width ofΔ₁=λ₁×2n_(eff1) in the direction of the primitive translation vector a₁.The phase of the resonance mode in the a₁ direction rotates by 180degrees at the phase shift structure, and therefore the profile of theperpendicular output beam becomes a single peak. FIG. 8B illustrates aschematic view of a far field and the polarization direction of thesurface emitting laser 100 of the third embodiment.

In the third embodiment, the phase shift has the width ofΔ₁=λ₁×2n_(eff1). The same effect is obtained when the relationalexpression Δ₁=s×(λ₁×2n_(eff1)) described by an odd number s more than 0is satisfied. In the third embodiment, although the two-dimensionalphotonic crystal layer includes one phase shift structure by way ofexample, alternatively, the two-dimensional photonic crystal layer mayinclude at least two phase shift structures.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2010-249158, filed Nov. 5, 2010, which is hereby incorporated byreference herein in its entirety.

1. A surface emitting laser comprising a two-dimensional photoniccrystal that includes a resonance mode in an in-plane direction, whereinthe two-dimensional photonic crystal includes two primitive translationvectors of a primitive translation vector a₁ and a primitive translationvector a₂, which extend in different directions, the resonance modeincludes at least a resonance mode resonating in a direction in whichthe primitive translation vector a₁ extends and a resonance moderesonating in a direction in which the primitive translation vector a₂extends, the primitive translation vector a₁ has a length |a₁|, theprimitive translation vector a₂ has a length |a₂|, the length |a₁|satisfies a relational expression |a₁|=p×(λ₁/2n_(eff1)) that isdescribed by a resonance wavelength λ₁ in the resonance mode in the a₁direction, an effective refractive index n_(eff1) determined by theresonance mode in the a₁ direction, and an integer p of 2 or more, thelength |a₂| satisfies a relational expression |a₂|=λ₂/2n_(eff2) that isdescribed by a resonance wavelength λ₂ in the resonance mode in the a₂direction and an effective refractive index n_(eff2) determined by theresonance mode in the a₂ direction, and the resonance wavelength λ₁ andthe resonance wavelength λ₂ satisfy a relational expressionλ₂≦2×(n_(eff2)/(n_(out)+n_(eff2)))×λ₁ that is described by the effectiverefractive index n_(eff2) and a refractive index n_(out) of an externalmedium located out of the surface emitting laser.
 2. The surfaceemitting laser according to claim 1, wherein the resonance wavelength λ₂in the resonance mode in the a₂ direction satisfies a relationalexpression λ_(S)≦λ₂≦λ₁ that is described by a shortest wavelength λ_(S)in a emission wavelength region of an active layer and the resonancewavelength λ₁.
 3. The surface emitting laser according to claim 1,wherein a gain of the active layer at the resonance wavelength λ₁ islarger than a gain of the active layer at the resonance wavelength λ₂.4. The surface emitting laser according to claim 2, further comprising amirror, which reflects light having the wavelengths of λ_(S) to λ₁ to again region, on an outside of the two-dimensional photonic crystal. 5.The surface emitting laser according to claim 1, wherein thetwo-dimensional photonic crystal includes at least one phase shiftstructure, having a width Δ₁, in the direction of the primitivetranslation vector a₁, and the width Δ₁ satisfies a relationalexpression Δ₁=s×(λ₁×2n_(eff1)) that is described by an odd number slarger than 0.